Open Research Index

N4Code: optimal finite-length block codes of size four for binary symmetric channels

Shenghao Yang, Yanyan Dong

Palomar Registrypalomar/PALOMAR-2026-09-05-000003Sep 5, 2026cs.ITscore 0

A Lean 4 and mathlib formalization of the Dong-Yang classification of optimal (n,4) binary block codes for binary symmetric channels. The registered results are Theorems 1-5 of the paper: existence of an optimal linear or Class-I code, the explicit linear optimal codes by residue class modulo 3, the universal strict-improvement reductions outside the linear, Class-I, and Class-II classes, the Class-I condition reduction to linear codes, and the finite classification for blocklengths 2 <= n <= 8. The Lean statements use the strict-improvement contrapositive forms.

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